Math 225 Multivariable Calculus and Analytic Geometry II  Spring 2012
              Instructor              Amites Sarkar
              Text                    Calculus: Multivariable (5th ed.)
                                      Hughes-Hallett et al.
              Calculator              TI-85 or higher
              Course content
              This course is a continuation of Multivariable Calculus I (MATH 224). We will cover
              Sections 16.3, 16.5, 16.7 and Chapters 17–20 of the book. The two main themes are
              analytic geometry and vector calculus. Vector calculus is central to many areas of
              theoretical physics: for instance, Maxwell’s equations, connecting electric and magnetic
              fields, are written in the language of vector calculus.
              Someofthemostuseful tools in vector calculus are Green’s theorem, Stokes’ theorem
              and the Divergence theorem. These are generalizations of the fundamental theorem of
              calculus. We will spend much time understanding and applying these theorems.
              Exams
              Midterm 1   Friday 20 April
              Midterm 2   Friday 18 May
              Final       Tuesday 5 June 8–10 am
              Grading
              The midterms are each worth 20%, and the final is worth 30%. In addition, there will be
              six 30 minute quizzes on 30 March, 6 April, 27 April, 4 May, 11 May, and 25 May, which
              are worth 5% each. If you feel too ill to take an exam, don’t take it, but bring a doctor’s
              certificate to me when you feel better and I will make arrangements.
              Office hours
              My office hours are 3–3:50 on Mondays, Tuesdays, Thursdays and Fridays, in 216 Bond
              Hall. My phone number is 650 7569 and my e-mail is amites.sarkar@wwu.edu
                   Course Objectives
                   The successful student will demonstrate:
                   1.  Understanding of the analytic ideas behind the definite integral of a multivariable
                   function, including its definition as a limit of Riemann sums.
                   2. Competenceinthecomputationofmultipleintegrals, includingintegrationincylindrical
                   and spherical coordinates, and the ability to choose a convenient system of coordinates.
                   3. Ability to use parametrization to represent curves and surfaces.
                   4. Ability to use parameterizations of curves to study the motion of a particle and to solve
                   geometric problems.
                   5. Understanding of the basic concept of a vector field, and familiarity with examples of
                   vector fields.
                   6. Ability to determine whether a vector field is the gradient of a function, and, if so, the
                   ability to find such a function.
                   7. CompetenceintheuseofGreen’stheorem,Stokes’theoremandtheDivergencetheorem.
                   8. Understanding of the analytic ideas and of the geometrical and physical interpretations
                   of line and flux integrals.
                   9. Competence in the computation of line and flux integrals.
                   10. Competence in the computation of the divergence and the curl of a vector field, and
                   understanding of their physical interpretations.
                   Relation to Overall Program Goals
                   Among other things, this course will (i) enhance your problem-solving skills; (ii) help you
                   recognize that a problem can have different useful representations (graphical, numerical,
                   or symbolic); (iii) increase your appreciation of the role of mathematics in the sciences and
                   the real world; (iv) inform you about the historical context of the area of mathematics
                   studied.